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The Steiner Ratio of L p -planes

In: Handbook of Combinatorial Optimization

Author

Listed:
  • Jens Albrecht

    (University of Greifswald, Institute of Mathematics and Computer Science)

  • Dietmar Cieslik

    (University of Greifswald, Institute of Mathematics and Computer Science)

Abstract

Starting with the famous book ”What is Mathematics” by Courant and Robbins the following problem has been popularized under the name of Steiner: For a given finite set of points in a metric space find a network which connects all points of the set with minimal length. Such a network must be a tree, which is called a Steiner Minimal Tree (SMT). It may contain vertices other than the points which are to be connected. Such points are called Steiner points.1 A classical survey of this problem in the Euclidean plane was given by Gilbert and Pollak [23]. An updated one can be found in [27].

Suggested Citation

  • Jens Albrecht & Dietmar Cieslik, 1999. "The Steiner Ratio of L p -planes," Springer Books, in: Ding-Zhu Du & Panos M. Pardalos (ed.), Handbook of Combinatorial Optimization, pages 573-589, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-3023-4_8
    DOI: 10.1007/978-1-4757-3023-4_8
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